Implications of model error for numerical climate prediction

Numerical climate models constitute the best available tools to tackle the problem of climate prediction. Two assumptions lie at the heart of their suitability: (1) a climate attractor exists, and (2) the numerical climate model's attractor lies on the actual climate attractor, or at least on the projection of the climate attractor on the model's phase space. In this contribution, the Lorenz '63 system is used both as a prototype system and as an imperfect model to investigate the implications of the second assumption. By comparing results drawn from the Lorenz '63 system and from numerical weather and climate models, the implications of using imperfect models for the prediction of weather and climate are discussed. It is shown that the imperfect model's orbit and the system's orbit are essentially different, purely due to model error and not to sensitivity to initial conditions. Furthermore, if a model is a perfect model, then the attractor, reconstructed by sampling a collection of initialised model orbits (forecast orbits), will be invariant to forecast lead time. This conclusion provides an alternative method for the assessment of climate models.

The potential of 1 h refractivity changes from an operational C-band magnetron-based radar for numerical weather prediction validation and data assimilation

Refractivity changes (ΔN) derived from radar ground clutter returns serve as a proxy for near-surface humidity changes (1 N unit ≡ 1% relative humidity at 20 °C). Previous studies have indicated that better humidity observations should improve forecasts of convection initiation. A preliminary assessment of the potential of refractivity retrievals from an operational magnetron-based C-band radar is presented. The increased phase noise at shorter wavelengths, exacerbated by the unknown position of the target within the 300 m gate, make it difficult to obtain absolute refractivity values, so we consider the information in 1 h changes. These have been derived to a range of 30 km with a spatial resolution of ∼4 km; the consistency of the individual estimates (within each 4 km × 4 km area) indicates that ΔN errors are about 1 N unit, in agreement with in situ observations. Measurements from an instrumented tower on summer days show that the 1 h refractivity changes up to a height of 100 m remain well correlated with near-surface values. The analysis of refractivity as represented in the operational Met Office Unified Model at 1.5, 4 and 12 km grid lengths demonstrates that, as model resolution increases, the spatial scales of the refractivity structures improve. It is shown that the magnitude of refractivity changes is progressively underestimated at larger grid lengths during summer. However, the daily time series of 1 h refractivity changes reveal that, whereas the radar-derived values are very well correlated with the in situ observations, the high-resolution model runs have little skill in getting the right values of ΔN in the right place at the right time. This suggests that the assimilation of these radar refractivity observations could benefit forecasts of the initiation of convection.

Impacts of increasing the aerosol complexity in the Met Office global numerical weather prediction model.

The inclusion of the direct and indirect radiative effects of aerosols in high-resolution global numerical weather prediction (NWP) models is being increasingly recognised as important for the improved accuracy of short-range weather forecasts. In this study the impacts of increasing the aerosol complexity in the global NWP configuration of the Met Office Unified Model (MetUM) are investigated. A hierarchy of aerosol representations are evaluated including three-dimensional monthly mean speciated aerosol climatologies, fully prognostic aerosols modelled using the CLASSIC aerosol scheme and finally, initialised aerosols using assimilated aerosol fields from the GEMS project. The prognostic aerosol schemes are better able to predict the temporal and spatial variation of atmospheric aerosol optical depth, which is particularly important in cases of large sporadic aerosol events such as large dust storms or forest fires. Including the direct effect of aerosols improves model biases in outgoing long-wave radiation over West Africa due to a better representation of dust. However, uncertainties in dust optical properties propagate to its direct effect and the subsequent model response. Inclusion of the indirect aerosol effects improves surface radiation biases at the North Slope of Alaska ARM site due to lower cloud amounts in high-latitude clean-air regions. This leads to improved temperature and height forecasts in this region. Impacts on the global mean model precipitation and large-scale circulation fields were found to be generally small in the short-range forecasts. However, the indirect aerosol effect leads to a strengthening of the low-level monsoon flow over the Arabian Sea and Bay of Bengal and an increase in precipitation over Southeast Asia. Regional impacts on the African Easterly Jet (AEJ) are also presented with the large dust loading in the aerosol climatology enhancing of the heat low over West Africa and weakening the AEJ. This study highlights the importance of including a more realistic treatment of aerosol–cloud interactions in global NWP models and the potential for improved global environmental prediction systems through the incorporation of more complex aerosol schemes.

Two fast radiative transfer methods to improve the temporal sampling of clouds in numerical weather prediction and climate models

The high computational cost of calculating the radiative heating rates in numerical weather prediction (NWP) and climate models requires that calculations are made infrequently, leading to poor sampling of the fast-changing cloud field and a poor representation of the feedback that would occur. This paper presents two related schemes for improving the temporal sampling of the cloud field. Firstly, the ‘split time-stepping’ scheme takes advantage of the independent nature of the monochromatic calculations of the ‘correlated-k’ method to split the calculation into gaseous absorption terms that are highly dependent on changes in cloud (the optically thin terms) and those that are not (optically thick). The small number of optically thin terms can then be calculated more often to capture changes in the grey absorption and scattering associated with cloud droplets and ice crystals. Secondly, the ‘incremental time-stepping’ scheme uses a simple radiative transfer calculation using only one or two monochromatic calculations representing the optically thin part of the atmospheric spectrum. These are found to be sufficient to represent the heating rate increments caused by changes in the cloud field, which can then be added to the last full calculation of the radiation code. We test these schemes in an operational forecast model configuration and find a significant improvement is achieved, for a small computational cost, over the current scheme employed at the Met Office. The ‘incremental time-stepping’ scheme is recommended for operational use, along with a new scheme to correct the surface fluxes for the change in solar zenith angle between radiation calculations.

Imbalanced land-surface water budgets in a numerical weather prediction system

There has been a significant increase in the skill and resolution of numerical weather prediction models (NWPs) in recent decades, extending the time scales of useful weather predictions. The land-surface models (LSMs) of NWPs are often employed in hydrological applications, which raises the question of how hydrologically representative LSMs really are. In this paper, precipitation (P), evaporation (E) and runoff (R) from the European Centre for Medium-Range Weather Forecasts (ECMWF) global models were evaluated against observational products. The forecasts differ substantially from observed data for key hydrological variables. In addition, imbalanced surface water budgets, mostly caused by data assimilation, were found on both global (P-E) and basin scales (P-E-R), with the latter being more important. Modeled surface fluxes should be used with care in hydrological applications and further improvement in LSMs in terms of process descriptions, resolution and estimation of uncertainties is needed to accurately describe the land-surface water budgets.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

The impact of a thermodynamic sea-ice module in the COSMO numerical weather prediction model on simulations for the Laptev Sea, Siberian Arctic

Previous versions of the Consortium for Small-scale Modelling (COSMO) numerical weather prediction model have used a constant sea-ice surface temperature, but observations show a high degree of variability on sub-daily timescales. To account for this, we have implemented a thermodynamic sea-ice module in COSMO and performed simulations at a resolution of 15 km and 5 km for the Laptev Sea area in April 2008. Temporal and spatial variability of surface and 2-m air temperature are verified by four automatic weather stations deployed along the edge of the western New Siberian polynya during the Transdrift XIII-2 expedition and by surface temperature charts derived from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data. A remarkable agreement between the new model results and these observations demonstrates that the implemented sea-ice module can be applied for short-range simulations. Prescribing the polynya areas daily, our COSMO simulations provide a high-resolution and high-quality atmospheric data set for the Laptev Sea for the period 14-30 April 2008. Based on this data set, we derive a mean total sea-ice production rate of 0.53 km3/day for all Laptev Sea polynyas under the assumption that the polynyas are ice-free and a rate of 0.30 km3/day if a 10-cm-thin ice layer is assumed. Our results indicate that ice production in Laptev Sea polynyas has been overestimated in previous studies.

Understanding advances in the simulation of the Madden-Julian Oscillation in a numerical weather prediction model.

The Madden-Julian Oscillation (MJO) is the dominant mode of intraseasonal variability in the Trop- ics. It can be characterised as a planetary-scale coupling between the atmospheric circulation and organised deep convection that propagates east through the equatorial Indo-Pacific region. The MJO interacts with weather and climate systems on a near-global scale and is a crucial source of predictability for weather forecasts on medium to seasonal timescales. Despite its global signifi- cance, accurately representing the MJO in numerical weather prediction (NWP) and climate models remains a challenge. This thesis focuses on the representation of the MJO in the Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasting (ECMWF), a state-of-the-art NWP model. Recent modifications to the model physics in Cycle 32r3 (Cy32r3) of the IFS led to ad- vances in the simulation of the MJO; for the first time the observed amplitude of the MJO was maintained throughout the integration period. A set of hindcast experiments, which differ only in their formulation of convection, have been performed between May 2008 and April 2009 to asses the sensitivity of MJO simulation in the IFS to the Cy32r3 convective parameterization. Unique to this thesis is the attribution of the advances in MJO simulation in Cy32r3 to the mod- ified convective parameterization, specifically, the relative-humidity-dependent formulation for or- ganised deep entrainment. Increasing the sensitivity of the deep convection scheme to environmen- tal moisture is shown to modify the relationship between precipitation and moisture in the model. Through dry-air entrainment, convective plumes ascending in low-humidity environments terminate lower in the atmosphere. As a result, there is an increase in the occurrence of cumulus congestus, which acts to moisten the mid-troposphere. Due to the modified precipitation-moisture relationship more moisture is able to build up which effectively preconditions the tropical atmosphere for the transition to deep convection. Results from this thesis suggest that a tropospheric moisture control on convection is key to simulating the interaction between the physics and large-scale circulation associated with the MJO.

Assimilation of Meteosat Second Generation (MSG) satellite data in a regional numerical weather prediction model using a one-dimensional variational approach

The quality of temperature and humidity retrievals from the infrared SEVIRI sensors on the geostationary Meteosat Second Generation (MSG) satellites is assessed by means of a one dimensional variational algorithm. The study is performed with the aim of improving the spatial and temporal resolution of available observations to feed analysis systems designed for high resolution regional scale numerical weather prediction (NWP) models. The non-hydrostatic forecast model COSMO (COnsortium for Small scale MOdelling) in the ARPA-SIM operational configuration is used to provide background fields. Only clear sky observations over sea are processed. An optimised 1D–VAR set-up comprising of the two water vapour and the three window channels is selected. It maximises the reduction of errors in the model backgrounds while ensuring ease of operational implementation through accurate bias correction procedures and correct radiative transfer simulations. The 1D–VAR retrieval quality is firstly quantified in relative terms employing statistics to estimate the reduction in the background model errors. Additionally the absolute retrieval accuracy is assessed comparing the analysis with independent radiosonde and satellite observations. The inclusion of satellite data brings a substantial reduction in the warm and dry biases present in the forecast model. Moreover it is shown that the retrieval profiles generated by the 1D–VAR are well correlated with the radiosonde measurements. Subsequently the 1D–VAR technique is applied to two three–dimensional case–studies: a false alarm case–study occurred in Friuli–Venezia–Giulia on the 8th of July 2004 and a heavy precipitation case occurred in Emilia–Romagna region between 9th and 12th of April 2005. The impact of satellite data for these two events is evaluated in terms of increments in the integrated water vapour and saturation water vapour over the column, in the 2 meters temperature and specific humidity and in the surface temperature. To improve the 1D–VAR technique a method to calculate flow–dependent model error covariance matrices is also assessed. The approach employs members from an ensemble forecast system generated by perturbing physical parameterisation schemes inside the model. The improved set–up applied to the case of 8th of July 2004 shows a substantial neutral impact.

Comparison of co-located independent ground-based middle atmospheric wind and temperature measurements with numerical weather prediction models

High-resolution, ground-based and independent observations including co-located wind radiometer, lidar stations, and infrasound instruments are used to evaluate the accuracy of general circulation models and data-constrained assimilation systems in the middle atmosphere at northern hemisphere midlatitudes. Systematic comparisons between observations, the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analyses including the recent Integrated Forecast System cycles 38r1 and 38r2, the NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalyses, and the free-running climate Max Planck Institute–Earth System Model–Low Resolution (MPI-ESM-LR) are carried out in both temporal and spectral dom ains. We find that ECMWF and MERRA are broadly consistent with lidar and wind radiometer measurements up to ~40 km. For both temperature and horizontal wind components, deviations increase with altitude as the assimilated observations become sparser. Between 40 and 60 km altitude, the standard deviation of the mean difference exceeds 5 K for the temperature and 20 m/s for the zonal wind. The largest deviations are observed in winter when the variability from large-scale planetary waves dominates. Between lidar data and MPI-ESM-LR, there is an overall agreement in spectral amplitude down to 15–20 days. At shorter time scales, the variability is lacking in the model by ~10 dB. Infrasound observations indicate a general good agreement with ECWMF wind and temperature products. As such, this study demonstrates the potential of the infrastructure of the Atmospheric Dynamics Research Infrastructure in Europe project that integrates various measurements and provides a quantitative understanding of stratosphere-troposphere dynamical coupling for numerical weather prediction applications.

Case studies of the effects of a total solar eclipse on weather with varying degrees of cloud cover using a local numerical weather prediction model

The importance of renewable energies for the European electricity market is growing rapidly. This presents transmission grids and the power market in general with new challenges which stem from the higher spatiotemporal variability of power generation. This uncertainty is due to the fact that renewable power production results from weather phenomena, thus making it difficult to plan and control. We present a sensitivity study of a total solar eclipse in central Europe in March. The weather in Germany and Europe was modeled using the German Weather Service's local area models COSMO-DE and COSMO-EU, respectively (http://www.cosmo-model.org/). The simulations were performed with and without considering a solar eclipse for the following 3 situations: 1. An idealized, clear-sky situation for the entire model area (Europe, COSMO-EU) 2. A real weather situation with mostly cloudy skies (Germany, COSMO-DE) 3. A real weather situation with mostly clear skies (Germany, COSMO-DE) The data should help to evaluate the effects of a total solar eclipse on the weather in the planetary boundary layer. The results show that a total solar eclipse has significant effects particularly on the main variables for renewable energy production, such as solar irradiation and temperature near the ground.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos

Prediction of wave refraction and shoaling using two numerical models /

"August 1981."

Wind power forecasts using Gaussian processes and numerical weather prediction

Since wind at the earth's surface has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safe and economic use of wind energy. In this paper, we investigated a combination of numeric and probabilistic models: a Gaussian process (GP) combined with a numerical weather prediction (NWP) model was applied to wind-power forecasting up to one day ahead. First, the wind-speed data from NWP was corrected by a GP, then, as there is always a defined limit on power generated in a wind turbine due to the turbine controlling strategy, wind power forecasts were realized by modeling the relationship between the corrected wind speed and power output using a censored GP. To validate the proposed approach, three real-world datasets were used for model training and testing. The empirical results were compared with several classical wind forecast models, and based on the mean absolute error (MAE), the proposed model provides around 9% to 14% improvement in forecasting accuracy compared to an artificial neural network (ANN) model, and nearly 17% improvement on a third dataset which is from a newly-built wind farm for which there is a limited amount of training data. © 2013 IEEE.